grandes-ecoles 2024 Q33

grandes-ecoles · France · x-ens-maths-d__mp Sequences and Series Evaluation of a Finite or Infinite Sum

Show the equality $$v_n(k) = \sum_{i=1}^{r} b_i e^{a_i} \int_{a_i}^{\infty} e^{-t} t^{n-kr} (t - a_1)^k \cdots (t - a_r)^k\, dt.$$

Show the equality
$$v_n(k) = \sum_{i=1}^{r} b_i e^{a_i} \int_{a_i}^{\infty} e^{-t} t^{n-kr} (t - a_1)^k \cdots (t - a_r)^k\, dt.$$